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General Formula for own price elasticity of demand P = Current price of good XP = Current price of good X X D = Quantity demanded at that priceX D = Quantity demanded at that price P = Small change in the current price P = Small change in the current price X D = Resulting change in quantity demanded X D = Resulting change in quantity demanded

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Arc Formula for Own Price Elasticity of Demand Get two points of the demand curve: Points A and B.Get two points of the demand curve: Points A and B. Consider P A and X A and P B and X B from the demand relationship.Consider P A and X A and P B and X B from the demand relationship. Note: well take absolute valueNote: well take absolute value

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Point Formula for Own Price Elasticity of Demand The exact formula for calculating an elasticity at the point A on the demand curve.The exact formula for calculating an elasticity at the point A on the demand curve. Note: well take absolute valueNote: well take absolute value

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Slope Compared to Elasticity The slope measures the rate of change of one variable (P, say) in terms of another (X, say).The slope measures the rate of change of one variable (P, say) in terms of another (X, say). The elasticity measures the percentage change of one variable (X, say) in terms of another (P, say).The elasticity measures the percentage change of one variable (X, say) in terms of another (P, say).

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Elasticities and Linear Demand The elasticity varies along a linear demand (or supply) curve. This is illustrated in the linear demand curve table above.The elasticity varies along a linear demand (or supply) curve. This is illustrated in the linear demand curve table above. Note: Usually we would report last column as absolute valueNote: Usually we would report last column as absolute value

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Perfectly Elastic Demand We say that demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded.We say that demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded. Price Quantity Perfectly Elastic Demand (elasticity = )

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Perfectly Inelastic Demand We say that demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded.We say that demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded. Price Quantity Perfectly Inelastic Demand (elasticity = 0)

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Perfectly Elastic Supply We say that supply is perfectly elastic when a 1% change in the price would result in an infinite change in quantity supplied.We say that supply is perfectly elastic when a 1% change in the price would result in an infinite change in quantity supplied. Price Quantity Perfectly Elastic Supply (elasticity = )

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Perfectly Inelastic Supply We say that supply is perfectly inelastic when a 1% change in the price would result in no change in quantity supplied.We say that supply is perfectly inelastic when a 1% change in the price would result in no change in quantity supplied. Price Quantity Perfectly Inelastic Supply (elasticity = 0)

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Determinants of elasticity What is a major determinant of the own price elasticity of demand?What is a major determinant of the own price elasticity of demand? Availability of substitutes in consumption. Availability of substitutes in consumption. What is a major determinant of the own price elasticity of supply?What is a major determinant of the own price elasticity of supply? Availability of alternatives in production. Availability of alternatives in production.

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Reminders Value of own price elasticity usually changes along a demand curveValue of own price elasticity usually changes along a demand curve there are many interesting intra elasticity applications there are many interesting intra elasticity applications Can also compare elasticities across marketsCan also compare elasticities across markets there are interesting inter elasticity questions there are interesting inter elasticity questions

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Elasticity and Total Expenditure (Graph) At the point M, the demand curve is unit elastic. M is the midpoint of this linear demand curveAt the point M, the demand curve is unit elastic. M is the midpoint of this linear demand curve Above M, demand is elastic, so total expenditure falls as the price risesAbove M, demand is elastic, so total expenditure falls as the price rises Below M, demand is inelastic. so total expenditure falls as price falls.Below M, demand is inelastic. so total expenditure falls as price falls. Total expenditure is maximized at the point M, where the elasticity = 1.Total expenditure is maximized at the point M, where the elasticity = 1. Price Quantity M Elasticity = 1: Total expenditure is at a maximum Elasticity > 1: Price reduction increases total expenditure; price increase reduces it. Elasticity < 1: Price reduction reduces total expenditure; price increase increases it.

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Change in Expenditure Components Old (price, quantity) is (P,Q).Old (price, quantity) is (P,Q). New (price, quantity) is (P*,Q*).New (price, quantity) is (P*,Q*). Expenditures increase if G is bigger than E.Expenditures increase if G is bigger than E. Since the point (P,Q) is above the midpoint of the linear demand curve, we know that total expenditures will increase at the lower price (P*,Q*). So, E must be smaller than G.Since the point (P,Q) is above the midpoint of the linear demand curve, we know that total expenditures will increase at the lower price (P*,Q*). So, E must be smaller than G. Price Quantity E F G P* P Q Q* Demand

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Own price elasticity and total revenue changes Total revenue (TR) is price times quantity. Along the demand curve P and Q move in opposite directions. Knowledge of Ed assists in knowing how TR will change.

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Elasticity and total revenue relationship When we look at the collection of consumers in the market, at this time in our study we assume each consumer pays the same price per unit for the product. Also at this time in our study the total expenditure of the consumers in the market would equal the total revenue (TR) to the sellers. So, here we look at the whole demand side of the market in general.

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Elasticity and total revenue relationship P Q P1 Q1 TR in the market is equal to the price in the market multiplied by the quantity traded in the market. In this diagram TR equals the area of the rectangle made by P1, Q1 and the horizontal and vertical axes. We know from math that the area of a rectangle is base times height and thus here that means P times Q.

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Elasticity and total revenue relationship We will want to look at the change in values of a variable and in order to do so we want to have a consistent measure of change. In this regard lets say the change in a variable is the later value minus the earlier value. Thus if the price should change from P1 to P2, then the change in price is P2 - P1, or similarly if the TR should change the change in TR is TR2 - TR1.

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Elasticity and total revenue relationship P Q P1 P2 Q1 Q2 Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c. The change in TR if the price should fall from P1 to P2 is (b + c) - (a + b) = c - a. Similarly, if the price should rise from P2 to P1 the change in TR is a - c. I will focus on price declines next. a b c

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Elasticity and total revenue relationship P Q P1 P2 Q1 Q2 Since the change in TR is c - a, the value of the change will depend on whether c is bigger or smaller, or even equal to, a. In this diagram we see c > a and thus the change in TR > 0. This means that as the price falls, TR rises. I think you will recall that in the upper left of the demand the demand is price elastic. Thus if the price falls in the elastic range of demand TR rises. a b c

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Elasticity and TR You will note on the previous screen that I had c - a. In the graph c is indicating the change in TR because we are selling more units. The area a is indicating the change in TR when there is a price change. We have to bring the two together to get the change in TR. Thus a lower price has a good and a bad. Good - sell more units. Bad - sell at lower price.

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Elasticity and total revenue relationship P Q P1 P2 Q1 Q2 Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c. In this diagram we see c < a and thus the change in TR < 0. I think you will recall that in the lower right of the demand the demand is price inelastic. Thus if the price falls in the inelastic range of demand TR falls. abab c

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Elasticity and total revenue relationship P Q P1P2P1P2 Q1 Q2 Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c. In this diagram we see c = a and thus the change in TR = 0. I think you will recall that in the middle of the demand the demand is unit elastic. Thus if the price falls in the unit elastic range of demand TR does not change. a b c

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Elasticity and TR P Q TR Q D When the price falls the quantity demanded always rises. As the quantity demanded rises (because of the price change) the TR is first rising in the elastic range, levels off when demand is unit elastic and TR falls in the inelastic range.

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Other Price Elasticities: Cross- Price Elasticity of Demand Elasticity of demand with respect to the price of a complementary good (cross-price elasticity)Elasticity of demand with respect to the price of a complementary good (cross-price elasticity) This elasticity is negative because as the price of a complementary good rises, the quantity demanded of the good itself falls. This elasticity is negative because as the price of a complementary good rises, the quantity demanded of the good itself falls. Example (from last week) software is complementary with computers. When the price of software rises the quantity demanded of computers falls. Example (from last week) software is complementary with computers. When the price of software rises the quantity demanded of computers falls. Cross-price elasticity quantifies this effect. Cross-price elasticity quantifies this effect.

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Other Price Elasticities: Cross Price Elasticity of Demand Elasticity of demand with respect to the price of a substitute good (also a cross-price elasticity)Elasticity of demand with respect to the price of a substitute good (also a cross-price elasticity) This elasticity is positive because as the price of a substitute good rises, the quantity demanded of the good itself rises. This elasticity is positive because as the price of a substitute good rises, the quantity demanded of the good itself rises. Example (from last week) hockey is substitute for basketball. When the price of hockey tickets rises the quantity demanded of basketball tickets rises. Example (from last week) hockey is substitute for basketball. When the price of hockey tickets rises the quantity demanded of basketball tickets rises. Cross-price elasticity quantifies this effect. Cross-price elasticity quantifies this effect.

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Other Elasticities: Income Elasticity of Demand The elasticity of demand with respect to a consumers income is called the income elasticity.The elasticity of demand with respect to a consumers income is called the income elasticity. When the income elasticity of demand is positive (normal good), consumers increase their purchases of the good as their incomes rise (e.g. automobiles, clothing). When the income elasticity of demand is positive (normal good), consumers increase their purchases of the good as their incomes rise (e.g. automobiles, clothing). When the income elasticity of demand is greater than 1 (luxury good), consumers increase their purchases of the good more than proportionate to the income increase (e.g. ski vacations). When the income elasticity of demand is greater than 1 (luxury good), consumers increase their purchases of the good more than proportionate to the income increase (e.g. ski vacations). When the income elasticity of demand is negative (inferior good), consumers reduce their purchases of the good as their incomes rise (e.g. potatoes). When the income elasticity of demand is negative (inferior good), consumers reduce their purchases of the good as their incomes rise (e.g. potatoes).

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From Individual Supply to Market Supply The supply of a good or service can be defined for an individual firm, or for a group of firms that make up a market or an industry.The supply of a good or service can be defined for an individual firm, or for a group of firms that make up a market or an industry. Market supply is the sum of all the quantities of a good or service supplied per period by all the firms selling in the market for that good or service.Market supply is the sum of all the quantities of a good or service supplied per period by all the firms selling in the market for that good or service.